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a b s t r a c tIn this paper, we obtain the annuli that contain all the zeros of the polynomial p(z) = a 0 + a 1 z + a 2 z 2 + · · · + a n z n , where a i 's are complex coefficients and z is a complex variable. Our results sharpen some of the recently obtained results in this direction. Also, we develop a MATLAB code to show that for some polynomials the bounds obtained by our results are considerably sharper than the bounds obtainable from the known results.

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